dist {mva} | R Documentation

## Distance Matrix Computation

### Description

This function computes and returns the distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix.

### Usage

    dist(x, method = "euclidean", diag = FALSE, upper = FALSE)

    as.dist(m, diag = FALSE, upper = FALSE)

    ## S3 method for class 'dist':
    print(x, diag = NULL, upper = NULL, ...)

    ## S3 method for class 'dist':
    as.matrix(x)

### Arguments

`x` | a numeric matrix, data frame or `"dist"` object.
`method` | the distance measure to be used. This must be one of `"euclidean"`, `"maximum"`, `"manhattan"`, `"canberra"` or `"binary"`. Any unambiguous substring can be given.
`diag` | logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist`.
`upper` | logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist`.
`m` | A matrix of distances to be converted to a `"dist"` object (only the lower triangle is used, the rest is ignored).
`...` | further arguments, passed to the (next) `print` method.

### Details

Available distance measures are (written for two vectors x and y):

`euclidean`:
  Usual square distance between the two vectors (2 norm).
`maximum`:
  Maximum distance between two components of x and y (supremum norm)
`manhattan`:
  Absolute distance between the two vectors (1 norm).
`canberra`:
  sum(|x_i - y_i| / |x_i + y_i|). Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.
`binary`:
  (aka asymmetric binary): The vectors are regarded as binary bits, so non-zero elements are ‘on’ and zero elements are ‘off’. The distance is the proportion of bits in which only one is on amongst those in which at least one is on.

Missing values are allowed, and are excluded from all computations involving the rows within which they occur. Further, when `Inf` values are involved, all pairs of values are excluded when their contribution to the distance gave `NaN` or `NA`.
If some columns are excluded in calculating a Euclidean, Manhattan or Canberra distance, the sum is scaled up proportionally to the number of columns used. If all pairs are excluded when calculating a particular distance, the value is `NA`.

The functions `as.matrix.dist()` and `as.dist()` can be used for conversion between objects of class `"dist"` and conventional distance matrices and vice versa.

### Value

An object of class `"dist"`.
The lower triangle of the distance matrix stored by columns in a vector, say `do`. If `n` is the number of observations, i.e., `n <- attr(do, "Size")`, then for i < j <= n, the dissimilarity between (row) i and j is `do[n*(i-1) - i*(i-1)/2 + j-i]`. The length of the vector is n*(n-1)/2, i.e., of order n^2.
The object has the following attributes (besides `"class"` equal to `"dist"`):

`Size` | integer, the number of observations in the dataset.
`Labels` | optionally, contains the labels, if any, of the observations of the dataset.
`Diag, Upper` | logicals corresponding to the arguments `diag` and `upper` above, specifying how the object should be printed.
`call` | optionally, the `call` used to create the object.
`methods` | optionally, the distance method used; resulting form `dist()`, the (`match.arg()`ed) `method` argument.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press.

### See Also

`daisy` in the cluster package with more possibilities in the case of mixed (contiuous / categorical) variables. `hclust`.

### Examples

    x <- matrix(rnorm(100), nrow=5)
    dist(x)
    dist(x, diag = TRUE)
    dist(x, upper = TRUE)
    m <- as.matrix(dist(x))
    d <- as.dist(m)
    stopifnot(d == dist(x))
    names(d) <- LETTERS[1:5]
    print(d, digits = 3)

    ## example of binary and canberra distances.
    x <- c(0, 0, 1, 1, 1, 1)
    y <- c(1, 0, 1, 1, 0, 1)
    dist(rbind(x,y), method="binary")
    ## answer 0.4 = 2/5
    dist(rbind(x,y), method="canberra")
    ## answer 2 * (6/5)

    ## Examples involving "Inf" :

    ## 1)
    x[6] <- Inf
    (m2 <- rbind(x,y))
    dist(m2, method="binary")# warning, answer 0.5 = 2/4
    ## These all give "Inf":
    stopifnot(Inf == dist(m2, method= "euclidean"),
              Inf == dist(m2, method= "maximum"),
              Inf == dist(m2, method= "manhattan"))
    ##  "Inf" is same as very large number:
    x1 <- x; x1[6] <- 1e100
    stopifnot(dist(cbind(x ,y), method="canberra") ==
        print(dist(cbind(x1,y), method="canberra")))

    ## 2)
    y[6] <- Inf #-> 6-th pair is excluded
    dist(rbind(x,y), method="binary")# warning; 0.5
    dist(rbind(x,y), method="canberra")#  3
    dist(rbind(x,y), method="maximum")  # 1
    dist(rbind(x,y), method="manhattan")# 2.4

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